Plasmonic-nanowire near-field beam analyzer

3.1 Calibration of the spatial resolution

As shown in Figure 3(a), two AuNW-fiber taper coupling units are used to set up a tip-to-tip structure for the calibration of the beam detection resolution. The detection light used was an L-band amplified spontaneous emission source (ASE) (1596 nm, 100 μW). The two AuNWs used had very similar dimensions, with a thickness of 130 nm and a height of 96 nm, as measured by the AFM. The left one serves as the target nanowire, and the right one serves as the detection nanowire, which can realize 3D light scanning and collection in the air. To achieve accurate beam detection, its scanning plane is set to be perpendicular to the wave vector of emitted beam from the target nanowire. Similar to the slit in a spectrometer or the hole in an aperture probe, the spatial resolution of the AuNW probe is primarily determined by its tip size, so AuNWs with smaller cross-sectional tip sizes are selected in this experiment. The beams emitted from different sample end faces are not always ideally symmetrical Gaussian shapes, so we need to define the beam radii (or beam half-width) of the sample beams on the x-axis and y-axis respectively, both of which are half the distance between two points on the light intensity distribution curve where the relative light intensity is 1/e ² of the peak value.

Figure 3:

Calibration of the spatial resolution. (a) Microscope image of two similarly sized nanowire probes in a tip-to-tip structure (scale bar, 10 μm). (b) Transmitted intensity profiles at the minimum distance condition, with the cross-sections of the peak intensity profiles along the x-axis direction and the y-axis direction (red points), and their Gaussian fitting curve (black line).

The measured transmission intensity map is shown in Figure 3(b), in which the transmission intensity fields along the x-axis and y-axis are both well fitted by Gaussian distributions. The x-axis and y-axis in the figure represent the short-axis and long-axis directions of the detection beam, rather than the horizontal and vertical directions in the spatial distribution. The distortion of field distributions along the y-axis direction may be due to environmental vibration. Vibration in the z-axis will cause jitter in the gap between the probe and the sample, while vibration in the x-axis or y-axis will cause blurring of the measurement image, both of which will lead to a reduction in spatial resolution. Taking the measurement data along the x-axis as an example, the beam half-width of the transmitted beam is calculated to be 269 nm. Since the cross-sectional dimensions of the emitting and collecting nanowires are almost the same, the beam half-width of the AuNW-fiber taper coupling structure can be calculated as 1 / 2 times the measured profile beam half-width. That is, the corrected spatial resolution of the AuNW probe along the x-axis is 190 nm (see Supplementary Note 3), which is less than one-eighth of the light wavelength. The y-axis analysis follows the same approach, with a probe spatial resolution of 238 nm.

3.2 3D spatial distribution evolution of output beams

To investigate the system’s 3D analysis capability, an AuNW with a diameter of 586 nm was selected as a new target sample. Its diameter is approximately five times the diameter of the right detection nanowire in Figure 3(a), which is similar to the size requirement of the aperture probe in the pinhole scanning method. Surface plasmons along the nanowire were also excited by the ASE source guided through a fiber taper. After 3D scanning, we obtained a series of typical transmitted light field intensity distribution maps at different distances, as shown in Figure 4(a). The optical signal is first transmitted in the AuNW in the form of surface plasmons, then emits at the end face and enters the air for further transmission. Remarkably, at the nanowire tip apex, the localized surface plasmons result in a highly confined electromagnetic field that is confined to a short distance from the tip apex and decays rapidly (see Figure S3), exhibiting a distance-dependent divergent evolution phenomenon. To further study the evolution characteristics of the beam spatial distribution, two transmitted light field intensity distribution maps at the distances of 25 nm and 1 μm are extracted, as shown in Figure 4(b) and (c), which are in the plasmonic hotspot region and the optical transmission region, respectively. The beam waist radii of the two-dimensional Gaussian fit in Figure 4(b) were calculated to be about 561 nm in the x-axis direction and 500 nm in the y-axis direction, with an ellipticity of 0.109. And those in Figure 4(c) were calculated to be about 1.187 μm in the x-axis direction and 1.022 μm in the y-axis direction, with an ellipticity of 0.139.

Figure 4:

3D spatial distribution evolution of the AuNW output beam along (a) z-axis direction, and transmitted light field intensity distribution maps at the distances of (b) 25 nm and (c) 1 μm, respectively. The beam parameters change versus propagation distance: (d) beam radii along the x-axis (black square) and the y-axis (red circle), and (e) the ellipticity of the beam spatial profile.

In the region of local enhancement of the SPP signal located near the nanowire tip apex (plasma hotspot region) [41], the beam widths decays rapidly with a near exponential divergence until reaching a distance of about 250 nm from the nanowire tip apex, as shown in Figure 4(d). As the distance continues to increases, the beam begins to diverge linearly with distance (inset of Figure 4(d)), as is usually measured in the far-field region. The slopes of the linear fits to the x-axis and y-axis beam radii in this region are 0.884 and 0.684, respectively, corresponding to the beam divergence angles of 41.5° and 34.4°, respectively. The difference of calculated values between x-axis and y-axis may be caused by the geometry of nanowires and the axis misalignment between the sample and probe nanowires during 3D scanning.

Similar to the beam width, the ellipticity of the sample beam spatial profile also undergoes an evolution from plasmon transmission to free-space transmission, which is shown in Figure 4(e) with a distance-dependent evolution characteristic. The beam profile at the AuNW end face is closely related to its size, and the beam transmitted in the far field shares similar transmission characteristics with the usual lens-focused beam, but its ellipticity gradually increases due to different beam divergence angles on the x and y-axis. The measurement errors of the beam width and ellipticity in the plasma hot spot area may be due to positioning errors of the nano-positioning stage and environment disturbance. Since the existence of the axis misalignment, the ellipticity of the measurement beam increases with the increasing measurement distance. However, the beam analysis system still has relatively accurate measurement capabilities within 1 μm distance, with an ellipticity error of 0.037. Beyond this range, the divergence distortion may occur.

The M ² factor is also an important evaluation index for beam analysis. For an ideal Gaussian beam, the product of the beam width at the waist and the beam divergence angle is usually constant. When taking the end face of the AuNW as the beam waist for beam analysis, due to the existence of the plasmonic hotspot region, spatial distribution size of the beam is usually smaller than that of the lens-focused beam or the ordinary single-mode fiber beam, thus the M ² factors of this AuNW were calculated to be 0.884 in the x-axis direction and 0.684 in the y-axis direction, which are lower than that of the ideal Gaussian beam (M ² = 1). This is one of the distinguishing characteristics of plasmonic nanowire output beams that are far below the diffraction limit. Thus, our analyzer system can obtain sufficient beam analysis parameter values with high accuracy. To the best of our knowledge, this is the first time that the beam evolution of a micro/nano-beam from the near-field region to the far-field region has been experimentally detected.

3.3 Complex mode analysis for thick nano-waveguides

To expand our study and uncover complex mode fields at sub-wavelengths, two extra thick nanoribbons with irregular end-face dimensions were also investigated. The irregularities at the end faces are mainly caused by the crystal growth mechanism of the metal. One nanoribbon with a width of 1.59 μm and a height of 85 nm was shown in Figure 5(a), and its measured beam intensity distribution was shown in Figure 5(b), exhibiting a typical multimode behavior with a two-spot spatial distribution. Larger waveguide with a width of 2.90 μm and a height of 92 nm, as shown in Figure 5(c), demonstrated more spots in beam spatial distribution. As shown in Figure 5(d), the minimum beam half-width of the multi-peak intensity fields (center spot) is measured to be ∼455 nm. In thick nano-waveguides, co-transmission multiple modes with different transmission losses can be supported, and they will then emit from the waveguide with different wavevector directions. However, these emitting multimodes are difficult to be measured and simulated directly. Here, we can simultaneously obtain beam near-field spatial distribution information of all modes in different micro/nano-waveguides without additional processing. And this application can also be extended to the characterizations of more waveguides with complex topography or end-face features, which allows us to deeply study the impact of geometric topography on the near-field emission characteristics of small-scale waveguides, and then explore new optical modes.

Figure 5:

Beam field intensity distributions of two thick Au nanoribbons with irregular end-face types. AFM images of the two nanoribbons end faces are shown in (a) and (c), and the measured corresponding intensity distributions are shown in (b) and (d), respectively.

3.4 Exploring diverse polarization modes

Our beam analysis system also demonstrated its potential in exploiting diverse polarization modes. Here the source was replaced by a tunable linearly polarized light source (TSL-550, Santec), whose wavelength was set to 1596 nm and an FPC was used to adjust its polarization state. For comparison, the samples in Figure 6(a) and (b) were a microfiber with a uniform diameter and a fiber taper with a sharp tip (tip diameter usually less than ∼100 nm), respectively, both of which had multimode transmission, thus beams emitted from the end faces of the fibers often contain multiple modes [20].

Figure 6:

Exploring diverse polarization modes. Microscope images of (a) a microfiber and (b) a fiber taper characterized by the plasmonic-nanowire probe of the beam analyzer (scale bar, 10 μm). Transmitted mode field distributions of the microfiber at two polarization states (c) 0° and (d) 90°. (e)–(h) Transmitted mode field distributions of the fiber taper as the input polarization state changed from 0° to 90°.

Figure 6(c) and (d) showed the output beam distributions of the microfiber in two mutually perpendicular polarization states at the same transmission distance. Different patterns were observed, confirming that they were derived from the fundamental mode and higher-order modes, respectively. To elaborate in more details, Figure 6(e)–(h) demonstrated the mode evolutions of vortex-like beam output from a fiber taper, by gradually changing the polarization per 90 degrees of its input light. Initially, the output beam detected by the analyzer probe in Figure 6(e) has the highest intensity spot at the center position (mainly fundamental mode), with a beam width of 4.6 μm. As the polarization state is adjusted, the intensity of the central spot weakens, and a clear vortex-like light field distribution appears. The light field energy at large ring radii gradually increases (shown in Figure 6(f) and (g)), i.e., the light field energy in the higher-order modes gradually increases. When the polarization state of the incident light is rotated by π/2, the energy of the vortex-like beam returns to the area with a smaller ring radius and is asymmetrical, as shown in Figure 6(h), where both higher-order modes and the fundamental mode propagating in the waveguide experience greater attenuation. When continuing to rotate the polarization state of the incident light by another π/2, the output beam distribution returns to the initial state shown in Figure 6(e), suggesting a polarization adjusting period of π. Thus, by analyzing the polarization-dependent spatial distributions of the vortex-like beam output, we can explore various new modes that are difficult to be predicted by numerical simulations.

5.1 Hybrid structure fabrication and distance calibration

As-fabricated AuNWs were first transferred in parallel by micromanipulation to the tip of the suspended silica optical fiber tapers on an MgF₂ substrate. To efficiently excite the plasmon propagation in AuNWs, we used an evanescent-wave coupling technique [4], [16], [17], [37–40]. In our approach, excitation light was first coupled into a standard silica fiber (SMF-28, Corning) and then squeezed into a fiber taper with a tip diameter of less than 100 nm. The fiber tapers were drawn from the standard optical fiber by using a simple flame-heated method [34,36 39 40], and then were bound to an MgF₂ substrate using a low-index UV-cured fluoropolymer. The tip of the fiber taper was protruded out of the substrate with a distance of 120 μm. The AuNWs were picked up from the growth substrates by a fiber taper with a sharp tip via micromanipulation and placed parallelly at the tip of the suspended silica fiber taper in air.

To calibrate the distance between the AuNW probe and the sample, an “approach and retreat” method was used (see Supplementary Note 1). A tunable narrow-linewidth light source (TSL-550, Santec) with a wavelength of 1550 nm and a power stability of ±0.05 dB/8 h was employed as the excitation light source. After a fiber polarization controller (FPC), a circulator (ports 1 to 2), and a fiber taper, the emitted light excited the plasmonic-nanowire probe. The reflection light from the sample was also collected using the same probe and circulator, and directed to the photodetector 1 (PD1) (OE-300-IN-03, FEMTO) through a wavelength-division multiplexer (WDM).

5.2 Near-field beam characteristics and analysis

To investigate the system’s ability to analyze beam quality, the AuNW-fiber taper-MgF₂ structure was mounted on a triple-axis micromanipulator (P-611.3S, Physik Instrumente) for near-field beam scanning. It has a travel range of 100 μm, a system resolution of 1 nm (closed loop), and a unidirectional repeatability of ±10 nm in three dimensions. During the scanning, the distance calibration source was shut down. The AuNW positioned in the sample’s near-field region could capture the light field intensity distribution of the beam at different scanning positions. Signals collected by the AuNW probe were directed to photodetector 2 (PD2) using an optical circulator and a WDM and then analyzed using an oscilloscope (OSC) module (NI PXI-5152, National Instruments) and a computer.